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Search: id:A139214
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| A139214 |
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Expansion of q * psi(q^2) * psi(-q^9) / (phi(-q^3) * psi(-q^3)) in powers of q where phi(), psi() are Ramanujan theta functions. |
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+0
5
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| 1, 0, 1, 3, 0, 3, 8, 0, 7, 18, 0, 15, 38, 0, 30, 75, 0, 57, 140, 0, 104, 252, 0, 183, 439, 0, 313, 744, 0, 522, 1232, 0, 852, 1998, 0, 1365, 3182, 0, 2150, 4986, 0, 3336, 7700, 0, 5106, 11736, 0, 7719, 17673, 0, 11538, 26322, 0, 17067, 38808, 0, 25004, 56682, 0
(list; graph; listen)
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OFFSET
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1,4
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FORMULA
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Expansion of eta(q^4)^2 * eta(q^6)^2 * eta(q^9) * eta(q^36) / (eta(q^2) * eta(q^3)^3 * eta(q^12) * eta(q^18)) in powers of q.
a(3*n + 1) = 0.
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = (1/4) g(t) where q = exp(2 pi i t) and g() is g.f. for A139216.
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EXAMPLE
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q + q^3 + 3*q^4 + 3*q^6 + 8*q^7 + 7*q^9 + 18*q^10 + 15*q^12 + 38*q^13 + ...
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PROGRAM
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(PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^4 + A)^2 * eta(x^6 + A)^2 * eta(x^9 + A) * eta(x^36 + A) / (eta(x^2 + A) * eta(x^3 + A)^3 * eta(x^12 + A) * eta(x^18 + A)), n))}
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CROSSREFS
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A139213(n) = 2 * a(n) unless n=0.
Sequence in context: A127803 A021771 A154853 this_sequence A010030 A117940 A099093
Adjacent sequences: A139211 A139212 A139213 this_sequence A139215 A139216 A139217
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Apr 11 2008
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